{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "a1921d43",
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import sympy as sp\n",
    "import sympy  as sp\n",
    "from sympy.matrices import Matrix\n",
    "from functools import partial\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits import mplot3d\n",
    "from math import pi\n",
    "import pprint\n",
    "pp=pprint.PrettyPrinter(indent=5)\n",
    "\n",
    "x,y,z,r,o=sp.symbols(\"x y z r theta\")\n",
    "#Tool Velocity Matrix\n",
    "\n",
    "\n",
    "X_BR=sp.Matrix([[200*sp.sin((2*np.pi*o)/50)*(2*np.pi/5)],[0],[200*sp.cos((2*np.pi*o)/50)*(2*np.pi/5)],[0],[0],[0]])\n",
    "X1_BR=sp.Matrix([[-160],[0],[0],[0],[0],[0]])\n",
    "X2_BR=sp.Matrix([[-40],[0],[0],[0],[0],[0]])\n",
    "\n",
    "X_FR=sp.Matrix([[200*sp.sin((2*np.pi*o)/50)*(2*np.pi/5)],[0],[200*sp.cos((2*np.pi*o)/50)*(2*np.pi/5)],[0],[0],[0]])\n",
    "X1_FR=sp.Matrix([[-160],[0],[0],[0],[0],[0]])\n",
    "X2_FR=sp.Matrix([[-40],[0],[0],[0],[0],[0]])\n",
    "\n",
    "X_BL=sp.Matrix([[200*sp.sin((2*np.pi*o)/50)*(2*np.pi/5)],[0],[200*sp.cos((2*np.pi*o)/50)*(2*np.pi/5)],[0],[0],[0]])\n",
    "X1_BL=sp.Matrix([[-160],[0],[0],[0],[0],[0]])\n",
    "X2_BL=sp.Matrix([[-40],[0],[0],[0],[0],[0]])\n",
    "\n",
    "X_FL=sp.Matrix([[200*sp.sin((2*np.pi*o)/50)*(2*np.pi/5)],[0],[200*sp.cos((2*np.pi*o)/50)*(2*np.pi/5)],[0],[0],[0]])\n",
    "X1_FL=sp.Matrix([[-160],[0],[0],[0],[0],[0]])\n",
    "X2_FL=sp.Matrix([[-40],[0],[0],[0],[0],[0]])\n",
    "\n",
    "\n",
    "file_name='front_jump_gait.json'\n",
    "\n",
    "theta_i, alpha_i, d_i, a_i, A_i, a_3, d_1, d_3, d_5, d_7 = sp.symbols('theta_i alpha_i d_i a_i A_i a_3 d_1, d_3, d_5, d_7')\n",
    "theta_1,theta_2,theta_3,theta_4,theta_5,theta_6,theta_7 = sp.symbols ('theta_1,theta_2, theta_3, theta_4, theta_5, theta_6, theta_7')\n",
    "Rot_z = sp.Matrix([ [sp.cos(theta_i), -sp.sin(theta_i),0,0], [sp.sin(theta_i),sp.cos(theta_i),0,0], [0,0,1,0], [0,0,0,1] ]);\n",
    "Rot_x = sp.Matrix([ [1,0,0,0], [0,sp.cos(alpha_i), -sp.sin(alpha_i),0], [0, sp.sin(alpha_i), sp.cos(alpha_i), 0], [0,0,0,1] ]); \n",
    "Tran_z = sp.Matrix([[1,0,0,0], [0,1,0,0], [0,0,1,d_i], [0,0,0,1]])\n",
    "Tran_x = sp.Matrix([[1,0,0,a_i], [0,1,0,0], [0,0,1,0], [0,0,0,1]])\n",
    "\n",
    "A_i=Rot_z*Tran_z*Tran_x*Rot_x\n",
    "\n",
    "# Back Left Leg\n",
    "\n",
    "BL_Ad0=A_i.subs([(theta_i,math.radians(90)),(alpha_i,math.radians(90)),(a_i,0),(d_i,0)])\n",
    "BL_A1=A_i.subs([(theta_i,theta_1),(alpha_i,math.radians(0)),(a_i,0),(d_i,0)])\n",
    "BL_Ad1=A_i.subs([(theta_i,math.radians(-90)),(alpha_i,math.radians(90)),(a_i,0),(d_i,64.85)])\n",
    "BL_A2=A_i.subs([(theta_i,theta_2),(alpha_i,math.radians(0)),(a_i,0),(d_i,-140)])\n",
    "BL_Ad2=A_i.subs([(theta_i,math.radians(0)),(alpha_i,math.radians(0)),(a_i,500),(d_i,0)])\n",
    "BL_A3=A_i.subs([(theta_i,theta_3),(alpha_i,math.radians(0)),(a_i,0),(d_i,0)])\n",
    "BL_A4=A_i.subs([(theta_i,0),(alpha_i,math.radians(0)),(a_i,450),(d_i,0)])\n",
    "\n",
    "# Back Right Leg\n",
    "BR_Ad0=A_i.subs([(theta_i,math.radians(-90)),(alpha_i,math.radians(90)),(a_i,0),(d_i,0)])\n",
    "BR_A1=A_i.subs([(theta_i,theta_1),(alpha_i,math.radians(0)),(a_i,0),(d_i,0)])\n",
    "BR_Ad1=A_i.subs([(theta_i,math.radians(-90)),(alpha_i,math.radians(-90)),(a_i,0),(d_i,64.85)])\n",
    "BR_A2=A_i.subs([(theta_i,theta_2),(alpha_i,math.radians(0)),(a_i,0),(d_i,140)])\n",
    "BR_Ad2=A_i.subs([(theta_i,math.radians(0)),(alpha_i,math.radians(0)),(a_i,500),(d_i,0)])\n",
    "BR_A3=A_i.subs([(theta_i,theta_3),(alpha_i,math.radians(0)),(a_i,0),(d_i,0)])\n",
    "BR_A4=A_i.subs([(theta_i,0),(alpha_i,math.radians(0)),(a_i,450),(d_i,0)])\n",
    "\n",
    "\n",
    "#Front Left Leg\n",
    "FL_Ad0=A_i.subs([(theta_i,math.radians(90)),(alpha_i,math.radians(90)),(a_i,0),(d_i,0)])\n",
    "FL_A1=A_i.subs([(theta_i,theta_1),(alpha_i,math.radians(0)),(a_i,0),(d_i,0)])\n",
    "FL_Ad1=A_i.subs([(theta_i,math.radians(-90)),(alpha_i,math.radians(90)),(a_i,0),(d_i,64.85)])\n",
    "FL_A2=A_i.subs([(theta_i,theta_2),(alpha_i,math.radians(0)),(a_i,0),(d_i,-140)])\n",
    "FL_Ad2=A_i.subs([(theta_i,math.radians(0)),(alpha_i,math.radians(0)),(a_i,500),(d_i,0)])\n",
    "FL_A3=A_i.subs([(theta_i,theta_3),(alpha_i,math.radians(0)),(a_i,0),(d_i,0)])\n",
    "FL_A4=A_i.subs([(theta_i,0),(alpha_i,math.radians(0)),(a_i,450),(d_i,0)])\n",
    "\n",
    "\n",
    "#Front Right Leg\n",
    "FR_Ad0=A_i.subs([(theta_i,math.radians(-90)),(alpha_i,math.radians(90)),(a_i,0),(d_i,0)])\n",
    "FR_A1=A_i.subs([(theta_i,theta_1),(alpha_i,math.radians(0)),(a_i,0),(d_i,0)])\n",
    "FR_Ad1=A_i.subs([(theta_i,math.radians(-90)),(alpha_i,math.radians(-90)),(a_i,0),(d_i,-64.85)])\n",
    "FR_A2=A_i.subs([(theta_i,theta_2),(alpha_i,math.radians(0)),(a_i,0),(d_i,140)])\n",
    "FR_Ad2=A_i.subs([(theta_i,math.radians(0)),(alpha_i,math.radians(0)),(a_i,500),(d_i,0)])\n",
    "FR_A3=A_i.subs([(theta_i,theta_3),(alpha_i,math.radians(0)),(a_i,0),(d_i,0)])\n",
    "FR_A4=A_i.subs([(theta_i,0),(alpha_i,math.radians(0)),(a_i,450),(d_i,0)])\n",
    "\n",
    "\n",
    "T1=BR_Ad0*BR_A1\n",
    "T2=BR_Ad0*BR_A1*BR_Ad1*BR_A2\n",
    "T3=BR_Ad0*BR_A1*BR_Ad1*BR_A2*BR_Ad2*BR_A3\n",
    "T4=BR_Ad0*BR_A1*BR_Ad1*BR_A2*BR_Ad2*BR_A3*BR_A4\n",
    "\n",
    "Z0 = T1[:3,2]\n",
    "Z1 = T2[:3,2]\n",
    "Z2 = T3[:3,2]\n",
    "Z3 = T4[:3,2]\n",
    "Xp=T4[:3,3]\n",
    "diff_thet_1 = Xp.diff(theta_1) #Partially differentiating Xp wrt θ1\n",
    "diff_thet_2 = Xp.diff(theta_2) #Partially differentiating Xp wrt θ2\n",
    "diff_thet_3 = Xp.diff(theta_3) #Partially differentiating Xp wrt θ4\n",
    "J_BR = Matrix([[diff_thet_1[0],diff_thet_2[0],diff_thet_3[0]],\n",
    "          [diff_thet_1[1],diff_thet_2[1],diff_thet_3[1]],\n",
    "          [diff_thet_1[2],diff_thet_2[2],diff_thet_3[2]],\n",
    "          [Z0[0],Z1[0],Z2[0]],[Z0[1],Z1[1],Z2[1]],[Z0[2],Z1[2],Z2[2]]])\n",
    "\n",
    "T1=BL_Ad0*BL_A1\n",
    "T2=BL_Ad0*BL_A1*BL_Ad1*BL_A2\n",
    "T3=BL_Ad0*BL_A1*BL_Ad1*BL_A2*BL_Ad2*BL_A3\n",
    "T4=BL_Ad0*BL_A1*BL_Ad1*BL_A2*BL_Ad2*BL_A3*BL_A4\n",
    "\n",
    "Z0 = T1[:3,2]\n",
    "Z1 = T2[:3,2]\n",
    "Z2 = T3[:3,2]\n",
    "Z3 = T4[:3,2]\n",
    "Xp=T4[:3,3]\n",
    "diff_thet_1 = Xp.diff(theta_1) #Partially differentiating Xp wrt θ1\n",
    "diff_thet_2 = Xp.diff(theta_2) #Partially differentiating Xp wrt θ2\n",
    "diff_thet_3 = Xp.diff(theta_3) #Partially differentiating Xp wrt θ4\n",
    "J_BL = Matrix([[diff_thet_1[0],diff_thet_2[0],diff_thet_3[0]],\n",
    "          [diff_thet_1[1],diff_thet_2[1],diff_thet_3[1]],\n",
    "          [diff_thet_1[2],diff_thet_2[2],diff_thet_3[2]],\n",
    "          [Z0[0],Z1[0],Z2[0]],[Z0[1],Z1[1],Z2[1]],[Z0[2],Z1[2],Z2[2]]])\n",
    "\n",
    "T1=FL_Ad0*FL_A1\n",
    "T2=FL_Ad0*FL_A1*FL_Ad1*FL_A2\n",
    "T3=FL_Ad0*FL_A1*FL_Ad1*FL_A2*FL_Ad2*FL_A3\n",
    "T4=FL_Ad0*FL_A1*FL_Ad1*FL_A2*FL_Ad2*FL_A3*FL_A4\n",
    "\n",
    "Z0 = T1[:3,2]\n",
    "Z1 = T2[:3,2]\n",
    "Z2 = T3[:3,2]\n",
    "Z3 = T4[:3,2]\n",
    "Xp=T4[:3,3]\n",
    "diff_thet_1 = Xp.diff(theta_1) #Partially differentiating Xp wrt θ1\n",
    "diff_thet_2 = Xp.diff(theta_2) #Partially differentiating Xp wrt θ2\n",
    "diff_thet_3 = Xp.diff(theta_3) #Partially differentiating Xp wrt θ4\n",
    "J_FL = Matrix([[diff_thet_1[0],diff_thet_2[0],diff_thet_3[0]],\n",
    "          [diff_thet_1[1],diff_thet_2[1],diff_thet_3[1]],\n",
    "          [diff_thet_1[2],diff_thet_2[2],diff_thet_3[2]],\n",
    "          [Z0[0],Z1[0],Z2[0]],[Z0[1],Z1[1],Z2[1]],[Z0[2],Z1[2],Z2[2]]])\n",
    "\n",
    "T1=FR_Ad0*FR_A1\n",
    "T2=FR_Ad0*FR_A1*FR_Ad1*FR_A2\n",
    "T3=FR_Ad0*FR_A1*FR_Ad1*FR_A2*FR_Ad2*FR_A3\n",
    "T4=FR_Ad0*FR_A1*FR_Ad1*FR_A2*FR_Ad2*FR_A3*FR_A4\n",
    "\n",
    "Z0 = T1[:3,2]\n",
    "Z1 = T2[:3,2]\n",
    "Z2 = T3[:3,2]\n",
    "Z3 = T4[:3,2]\n",
    "Xp=T4[:3,3]\n",
    "diff_thet_1 = Xp.diff(theta_1) #Partially differentiating Xp wrt θ1\n",
    "diff_thet_2 = Xp.diff(theta_2) #Partially differentiating Xp wrt θ2\n",
    "diff_thet_3 = Xp.diff(theta_3) #Partially differentiating Xp wrt θ4\n",
    "J_FR = Matrix([[diff_thet_1[0],diff_thet_2[0],diff_thet_3[0]],\n",
    "          [diff_thet_1[1],diff_thet_2[1],diff_thet_3[1]],\n",
    "          [diff_thet_1[2],diff_thet_2[2],diff_thet_3[2]],\n",
    "          [Z0[0],Z1[0],Z2[0]],[Z0[1],Z1[1],Z2[1]],[Z0[2],Z1[2],Z2[2]]])\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "9a72d216",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing Trajectory\n",
      "............................................................................"
     ]
    }
   ],
   "source": [
    "dt=0.05  #Time difference\n",
    "t_1=[math.radians(0)]  #Theta 1\n",
    "t_2=[-0.7]  #Theta 2\n",
    "t_3=[1.5]  #Theta 4\n",
    "back_right_joint=[]\n",
    "T=T4\n",
    "x_tool_br=[]\n",
    "y_tool_br=[]\n",
    "z_tool_br=[]\n",
    "#Tool Velocity Matrix\n",
    "# X=sp.Matrix([[100*sp.sin((2*np.pi*o)/200)*(2*np.pi)/10],[0],[100*sp.cos((2*np.pi*o)/200)*(2*np.pi)/10],[0],[0],[0]])\n",
    "# X1=sp.Matrix([[-40],[0],[0],[0],[0],[0]])\n",
    "i=0\n",
    "j=0\n",
    "print(\"Computing Trajectory\")\n",
    "while i<=75:\n",
    "    if i>25:\n",
    "        X_eval=X_BR.subs(o,j)\n",
    "        j=j+1\n",
    "    if i>50:\n",
    "        X_eval=X1_BR.subs(o,j)\n",
    "    if i<25:\n",
    "        X_eval=X2_BR.subs(o,j)\n",
    "    back_right_joint.append([t_1[i],t_2[i],t_3[i]])\n",
    "    T_eval=T.subs([(theta_1,t_1[i]),(theta_2,t_2[i]),(theta_3,t_3[i])])\n",
    "    x_tool_br.append(T_eval[3])\n",
    "    y_tool_br.append(T_eval[7])\n",
    "    z_tool_br.append(T_eval[11])\n",
    "    J_eval=J_BR.subs([(theta_1,t_1[i]),(theta_2,t_2[i]),(theta_3,t_3[i])])\n",
    "    q=J_eval.pinv()*X_eval\n",
    "    q=q*dt\n",
    "#     print(q)\n",
    "    t_1.append(q[0]+t_1[i])\n",
    "    t_2.append(q[1]+t_2[i])\n",
    "    t_3.append(q[2]+t_3[i])\n",
    "    \n",
    "    print(\".\",end=\"\")\n",
    "    i=i+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "1e406526",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing Trajectory\n",
      "............................................................................"
     ]
    }
   ],
   "source": [
    "dt=0.05  #Time difference\n",
    "t_1=[math.radians(0)]  #Theta 1\n",
    "t_2=[-0.7]  #Theta 2\n",
    "t_3=[1.5]  #Theta 4\n",
    "front_right_joint=[]\n",
    "T=T4\n",
    "x_tool_fr=[]\n",
    "y_tool_fr=[]\n",
    "z_tool_fr=[]\n",
    "#Tool Velocity Matrix\n",
    "# X=sp.Matrix([[100*sp.sin((2*np.pi*o)/200)*(2*np.pi)/10],[0],[100*sp.cos((2*np.pi*o)/200)*(2*np.pi)/10],[0],[0],[0]])\n",
    "# X1=sp.Matrix([[-40],[0],[0],[0],[0],[0]])\n",
    "i=0\n",
    "j=0\n",
    "print(\"Computing Trajectory\")\n",
    "while i<=75:\n",
    "    if i>25:\n",
    "        X_eval=X_FR.subs(o,j)\n",
    "        j=j+1\n",
    "    if i>50:\n",
    "        X_eval=X1_FR.subs(o,j)\n",
    "    if i<25:\n",
    "        X_eval=X2_FR.subs(o,j)\n",
    "    front_right_joint.append([t_1[i],t_2[i],t_3[i]])\n",
    "    T_eval=T.subs([(theta_1,t_1[i]),(theta_2,t_2[i]),(theta_3,t_3[i])])\n",
    "    x_tool_fr.append(T_eval[3])\n",
    "    y_tool_fr.append(T_eval[7])\n",
    "    z_tool_fr.append(T_eval[11])\n",
    "    J_eval=J_FR.subs([(theta_1,t_1[i]),(theta_2,t_2[i]),(theta_3,t_3[i])])\n",
    "    q=J_eval.pinv()*X_eval\n",
    "    q=q*dt\n",
    "#     print(q)\n",
    "    t_1.append(q[0]+t_1[i])\n",
    "    t_2.append(q[1]+t_2[i])\n",
    "    t_3.append(q[2]+t_3[i])\n",
    "    \n",
    "    print(\".\",end=\"\")\n",
    "    i=i+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "3d70a9fc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing Trajectory\n",
      "............................................................................"
     ]
    }
   ],
   "source": [
    "dt=0.05  #Time difference\n",
    "t_1=[math.radians(0)]  #Theta 1\n",
    "t_2=[-0.7]  #Theta 2\n",
    "t_3=[1.5]  #Theta 4\n",
    "front_left_joint=[]\n",
    "T=T4\n",
    "x_tool_fl=[]\n",
    "y_tool_fl=[]\n",
    "z_tool_fl=[]\n",
    "#Tool Velocity Matrix\n",
    "# X=sp.Matrix([[100*sp.sin((2*np.pi*o)/200)*(2*np.pi)/10],[0],[100*sp.cos((2*np.pi*o)/200)*(2*np.pi)/10],[0],[0],[0]])\n",
    "# X1=sp.Matrix([[-40],[0],[0],[0],[0],[0]])\n",
    "i=0\n",
    "j=0\n",
    "print(\"Computing Trajectory\")\n",
    "while i<=75:\n",
    "    if i>25:\n",
    "        X_eval=X_FL.subs(o,j)\n",
    "        j=j+1\n",
    "    if i>50:\n",
    "        X_eval=X1_FL.subs(o,j)\n",
    "    if i<25:\n",
    "        X_eval=X2_FL.subs(o,j)\n",
    "    front_left_joint.append([t_1[i],t_2[i],t_3[i]])\n",
    "    T_eval=T.subs([(theta_1,t_1[i]),(theta_2,t_2[i]),(theta_3,t_3[i])])\n",
    "    x_tool_fl.append(T_eval[3])\n",
    "    y_tool_fl.append(T_eval[7])\n",
    "    z_tool_fl.append(T_eval[11])\n",
    "    J_eval=J_FL.subs([(theta_1,t_1[i]),(theta_2,t_2[i]),(theta_3,t_3[i])])\n",
    "    q=J_eval.pinv()*X_eval\n",
    "    q=q*dt\n",
    "#     print(q)\n",
    "    t_1.append(q[0]+t_1[i])\n",
    "    t_2.append(q[1]+t_2[i])\n",
    "    t_3.append(q[2]+t_3[i])\n",
    "    \n",
    "    print(\".\",end=\"\")\n",
    "    i=i+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "8f30a51c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing Trajectory\n",
      "............................................................................"
     ]
    }
   ],
   "source": [
    "dt=0.05  #Time difference\n",
    "t_1=[math.radians(0)]  #Theta 1\n",
    "t_2=[-0.7]  #Theta 2\n",
    "t_3=[1.5]  #Theta 4\n",
    "back_left_joint=[]\n",
    "T=T4\n",
    "x_tool_bl=[]\n",
    "y_tool_bl=[]\n",
    "z_tool_bl=[]\n",
    "#Tool Velocity Matrix\n",
    "# X=sp.Matrix([[100*sp.sin((2*np.pi*o)/200)*(2*np.pi)/10],[0],[100*sp.cos((2*np.pi*o)/200)*(2*np.pi)/10],[0],[0],[0]])\n",
    "# X1=sp.Matrix([[-40],[0],[0],[0],[0],[0]])\n",
    "i=0\n",
    "j=0\n",
    "print(\"Computing Trajectory\")\n",
    "while i<=75:\n",
    "    if i>25:\n",
    "        X_eval=X_BL.subs(o,j)\n",
    "        j=j+1\n",
    "    if i>50:\n",
    "        X_eval=X1_BL.subs(o,j)\n",
    "    if i<25:\n",
    "        X_eval=X2_BL.subs(o,j)\n",
    "    back_left_joint.append([t_1[i],t_2[i],t_3[i]])\n",
    "    T_eval=T.subs([(theta_1,t_1[i]),(theta_2,t_2[i]),(theta_3,t_3[i])])\n",
    "    x_tool_bl.append(T_eval[3])\n",
    "    y_tool_bl.append(T_eval[7])\n",
    "    z_tool_bl.append(T_eval[11])\n",
    "    J_eval=J_BL.subs([(theta_1,t_1[i]),(theta_2,t_2[i]),(theta_3,t_3[i])])\n",
    "    q=J_eval.pinv()*X_eval\n",
    "    q=q*dt\n",
    "#     print(q)\n",
    "    t_1.append(q[0]+t_1[i])\n",
    "    t_2.append(q[1]+t_2[i])\n",
    "    t_3.append(q[2]+t_3[i])\n",
    "    \n",
    "    print(\".\",end=\"\")\n",
    "    i=i+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "aebbe8d3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Create a grid of subplots with 2 rows and 2 columns\n",
    "fig, axs = plt.subplots(2, 2)\n",
    "\n",
    "# Plot 1: Top left subplot\n",
    "axs[0, 0].plot(x_tool_br, z_tool_br)\n",
    "axs[0, 0].set_xlabel(\"y coordinate\")\n",
    "axs[0, 0].set_ylabel(\"z coordinate\")\n",
    "axs[0, 0].set_title(\"Trajectory of Back Right Leg\")\n",
    "axs[0, 0].axis(\"equal\")\n",
    "axs[0, 0].grid(True)\n",
    "\n",
    "# Plot 2: Top right subplot\n",
    "axs[0, 1].plot(x_tool_bl, z_tool_bl)  # Replace with your desired plot\n",
    "axs[0, 1].set_xlabel(\"y\")\n",
    "axs[0, 1].set_ylabel(\"z\")\n",
    "axs[0, 1].set_title(\"Trajectory of Back Left Leg\")\n",
    "axs[0, 1].axis(\"equal\")\n",
    "axs[0, 1].grid(True)\n",
    "# Add other formatting and plotting commands as needed\n",
    "\n",
    "# Plot 3: Bottom left subplot\n",
    "axs[1, 0].plot(x_tool_fr, z_tool_fr)  # Replace with your desired plot\n",
    "axs[1, 0].set_xlabel(\"y\")\n",
    "axs[1, 0].set_ylabel(\"z\")\n",
    "axs[1, 0].set_title(\"Trajectory of Front Right Leg\")\n",
    "axs[1, 0].axis(\"equal\")\n",
    "axs[1, 0].grid(True)\n",
    "# Add other formatting and plotting commands as needed\n",
    "\n",
    "# Plot 4: Bottom right subplot\n",
    "axs[1, 1].plot(x_tool_fl, z_tool_fl)  # Replace with your desired plot\n",
    "axs[1, 1].set_xlabel(\"y\")\n",
    "axs[1, 1].set_ylabel(\"z\")\n",
    "axs[1, 1].set_title(\"Trajectory of Front Left Leg\")\n",
    "axs[1,1].axis(\"equal\")\n",
    "axs[1,1].grid(True)\n",
    "# Add other formatting and plotting commands as needed\n",
    "\n",
    "# Adjust the layout to avoid overlapping titles and labels\n",
    "fig.tight_layout()\n",
    "\n",
    "# Show the plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "4d3aa0e5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[0.0, -0.7, 1.5],\n",
       " [-1.41374293044852e-9, -0.702876631544616, 1.50000626606623],\n",
       " [-2.82887576970141e-9, -0.705745230679449, 1.49999470985377],\n",
       " [-4.24535162146106e-9, -0.708605749880216, 1.49996533126797],\n",
       " [-5.66312392780936e-9, -0.711458141552086, 1.49991813014646],\n",
       " [-7.08214647354450e-9, -0.714302358034348, 1.49985310625911],\n",
       " [-8.50237339398725e-9, -0.717138351605041, 1.49977025930782],\n",
       " [-9.92375918094403e-9, -0.719966074485555, 1.49966958892626],\n",
       " [-1.13462586876943e-8, -0.722785478845191, 1.49955109467951],\n",
       " [-1.27698271363630e-8, -0.725596516805683, 1.49941477606361],\n",
       " [-1.41944201231250e-8, -0.728399140445683, 1.49926063250507],\n",
       " [-1.56199936242763e-8, -0.731193301805211, 1.49908866336019],\n",
       " [-1.70465040025226e-8, -0.733978952890049, 1.49889886791443],\n",
       " [-1.84739080128339e-8, -0.736756045676112, 1.49869124538156],\n",
       " [-1.99021628076489e-8, -0.739524532113758, 1.49846579490284],\n",
       " [-2.13312259438134e-8, -0.742284364132065, 1.49822251554602],\n",
       " [-2.27610553875683e-8, -0.745035493643054, 1.49796140630430],\n",
       " [-2.41916095200783e-8, -0.747777872545872, 1.49768246609522],\n",
       " [-2.56228471432873e-8, -0.750511452730921, 1.49738569375941],\n",
       " [-2.70547274860977e-8, -0.753236186083939, 1.49707108805931],\n",
       " [-2.84872102088163e-8, -0.755952024490029, 1.49673864767775],\n",
       " [-2.99202554094420e-8, -0.758658919837641, 1.49638837121646],\n",
       " [-3.13538236288704e-8, -0.761356824022490, 1.49602025719455],\n",
       " [-3.27878758560980e-8, -0.764045688951436, 1.49563430404679],\n",
       " [-3.42223735339681e-8, -0.766725466546286, 1.49523051012192],\n",
       " [-3.56572785631826e-8, -0.769396108747563, 1.49480887368078],\n",
       " [-3.70925533093496e-8, -0.772057567518199, 1.49436939289441],\n",
       " [-2.84982687630446e-8, -0.790969341041965, 1.53334744777642],\n",
       " [-1.87063511845426e-8, -0.807224576154768, 1.57158758087303],\n",
       " [-7.69736490222839e-9, -0.820470369959396, 1.60855374884627],\n",
       " [4.53195605129227e-9, -0.830396889586483, 1.64372202761123],\n",
       " [1.79563877528850e-8, -0.836748931152672, 1.67658324453533],\n",
       " [3.25077283810906e-8, -0.839338602868788, 1.70664724320425],\n",
       " [4.80588623307917e-8, -0.838058293668730, 1.73344912968178],\n",
       " [6.44079275726939e-8, -0.832892621119666, 1.75655762078917],\n",
       " [8.12651786250931e-8, -0.823927654117265, 1.77558531662164],\n",
       " [9.82461317461746e-8, -0.811355513254500, 1.79020036204984],\n",
       " [1.14875064715458e-7, -0.795472612351211, 1.80013858756970],\n",
       " [1.30602353476095e-7, -0.776670418682595, 1.80521490495686],\n",
       " [1.44837057380905e-7, -0.755418658299168, 1.80533257525865],\n",
       " [1.56992734153933e-7, -0.732242191916815, 1.80048905295351],\n",
       " [1.66540544985557e-7, -0.707694006900634, 1.79077747599917],\n",
       " [1.73060738437005e-7, -0.682327544241287, 1.77638346866147],\n",
       " [1.76282946769696e-7, -0.656671653786483, 1.75757762079629],\n",
       " [1.76107914784583e-7, -0.631210827638336, 1.73470462947900],\n",
       " [1.72607617132744e-7, -0.606372224907207, 1.70817048482654],\n",
       " [1.66005622645220e-7, -0.582519731367125, 1.67842917769270],\n",
       " [1.56643374456564e-7, -0.559954234338908, 1.64597022414147],\n",
       " [1.44939791517903e-7, -0.538918635818307, 1.61130793244725],\n",
       " [1.31351226745577e-7, -0.519605903933319, 1.57497289875165],\n",
       " [1.16337008743745e-7, -0.502168576916797, 1.53750580430949],\n",
       " [1.00333447719942e-7, -0.486728437104455, 1.49945325650783],\n",
       " [9.53666448414560e-8, -0.500335501426890, 1.50472383649915],\n",
       " [9.03126831795240e-8, -0.513866371402855, 1.50970774622550],\n",
       " [8.51754154287852e-8, -0.527318936804468, 1.51440539543471],\n",
       " [7.99587229291505e-8, -0.540690976176139, 1.51881713483111],\n",
       " [7.46665115002982e-8, -0.553980161942494, 1.52294326222873],\n",
       " [6.93027067021920e-8, -0.567184065591964, 1.52678402829294],\n",
       " [6.38712485615223e-8, -0.580300162940271, 1.53033964188431],\n",
       " [5.83760858104724e-8, -0.593325839475324, 1.53361027501584],\n",
       " [5.28211696792272e-8, -0.606258395782494, 1.53659606743300],\n",
       " [4.72104472920983e-8, -0.619095053046802, 1.53929713082415],\n",
       " [4.15478547045602e-8, -0.631832958626167, 1.54171355266769],\n",
       " [3.58373096360604e-8, -0.644469191687695, 1.54384539972064],\n",
       " [3.00827039478246e-8, -0.657000768896845, 1.54569272115275],\n",
       " [2.42878959198676e-8, -0.669424650147373, 1.54725555132906],\n",
       " [1.84567023610376e-8, -0.681737744318117, 1.54853391224305],\n",
       " [1.25928906236502e-8, -0.693936915041027, 1.54952781560213],\n",
       " [6.70017056131019e-9, -0.706018986463307, 1.55023726456661],\n",
       " [7.82186480228558e-10, -0.717980748985187, 1.55066225514282],\n",
       " [-5.15749086739382e-9, -0.729818964953675, 1.55080277723085],\n",
       " [-1.11153721967410e-8, -0.741530374291595, 1.55065881532718],\n",
       " [-1.70880574723515e-8, -0.753111700040414, 1.55023034888205],\n",
       " [-2.30722435075081e-8, -0.764559653794685, 1.54951735231153],\n",
       " [-2.90647313498230e-8, -0.775870941005458, 1.54851979466407],\n",
       " [-3.50624334118190e-8, -0.787042266129718, 1.54723763894082]]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "front_left_joint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "cffe940f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[0.0, -0.7, 1.5],\n",
       " [-1.41374293044852e-9, -0.702876631544616, 1.50000626606623],\n",
       " [-2.82887576948457e-9, -0.705745230679449, 1.49999470985377],\n",
       " [-4.24535162135264e-9, -0.708605749880216, 1.49996533126797],\n",
       " [-5.66312392759252e-9, -0.711458141552086, 1.49991813014646],\n",
       " [-7.08214647332766e-9, -0.714302358034348, 1.49985310625911],\n",
       " [-8.50237339387883e-9, -0.717138351605041, 1.49977025930782],\n",
       " [-9.92375918083561e-9, -0.719966074485555, 1.49966958892626],\n",
       " [-1.13462586876943e-8, -0.722785478845191, 1.49955109467951],\n",
       " [-1.27698271362546e-8, -0.725596516805683, 1.49941477606361],\n",
       " [-1.41944201230166e-8, -0.728399140445683, 1.49926063250507],\n",
       " [-1.56199936240595e-8, -0.731193301805211, 1.49908866336019],\n",
       " [-1.70465040024142e-8, -0.733978952890049, 1.49889886791443],\n",
       " [-1.84739080127255e-8, -0.736756045676112, 1.49869124538156],\n",
       " [-1.99021628076489e-8, -0.739524532113758, 1.49846579490284],\n",
       " [-2.13312259439219e-8, -0.742284364132065, 1.49822251554602],\n",
       " [-2.27610553876767e-8, -0.745035493643054, 1.49796140630430],\n",
       " [-2.41916095201867e-8, -0.747777872545872, 1.49768246609522],\n",
       " [-2.56228471433957e-8, -0.750511452730921, 1.49738569375941],\n",
       " [-2.70547274863146e-8, -0.753236186083939, 1.49707108805931],\n",
       " [-2.84872102090331e-8, -0.755952024490029, 1.49673864767775],\n",
       " [-2.99202554096588e-8, -0.758658919837641, 1.49638837121646],\n",
       " [-3.13538236291957e-8, -0.761356824022490, 1.49602025719455],\n",
       " [-3.27878758565317e-8, -0.764045688951436, 1.49563430404679],\n",
       " [-3.42223735345102e-8, -0.766725466546286, 1.49523051012192],\n",
       " [-3.56572785638332e-8, -0.769396108747563, 1.49480887368078],\n",
       " [-3.70925533098917e-8, -0.772057567518199, 1.49436939289441],\n",
       " [-2.84982687649492e-8, -0.790969341041965, 1.53334744777642],\n",
       " [-1.87063511864472e-8, -0.807224576154768, 1.57158758087303],\n",
       " [-7.69736490347312e-9, -0.820470369959396, 1.60855374884627],\n",
       " [4.53195605004754e-9, -0.830396889586483, 1.64372202761123],\n",
       " [1.79563877513121e-8, -0.836748931152672, 1.67658324453533],\n",
       " [3.25077283795177e-8, -0.839338602868788, 1.70664724320425],\n",
       " [4.80588623287525e-8, -0.838058293668730, 1.73344912968178],\n",
       " [6.44079275711795e-8, -0.832892621119666, 1.75655762078917],\n",
       " [8.12651786235788e-8, -0.823927654117265, 1.77558531662164],\n",
       " [9.82461317446603e-8, -0.811355513254500, 1.79020036204984],\n",
       " [1.14875064714365e-7, -0.795472612351211, 1.80013858756970],\n",
       " [1.30602353475002e-7, -0.776670418682595, 1.80521490495686],\n",
       " [1.44837057380492e-7, -0.755418658299168, 1.80533257525865],\n",
       " [1.56992734153476e-7, -0.732242191916815, 1.80048905295351],\n",
       " [1.66540544985691e-7, -0.707694006900634, 1.79077747599917],\n",
       " [1.73060738437349e-7, -0.682327544241287, 1.77638346866147],\n",
       " [1.76282946770928e-7, -0.656671653786483, 1.75757762079629],\n",
       " [1.76107914785163e-7, -0.631210827638336, 1.73470462947900],\n",
       " [1.72607617133324e-7, -0.606372224907207, 1.70817048482654],\n",
       " [1.66005622646033e-7, -0.582519731367125, 1.67842917769270],\n",
       " [1.56643374456776e-7, -0.559954234338908, 1.64597022414147],\n",
       " [1.44939791517788e-7, -0.538918635818307, 1.61130793244725],\n",
       " [1.31351226744320e-7, -0.519605903933319, 1.57497289875165],\n",
       " [1.16337008740000e-7, -0.502168576916797, 1.53750580430949],\n",
       " [1.00333447715479e-7, -0.486728437104455, 1.49945325650783],\n",
       " [9.53666448374262e-8, -0.500335501426890, 1.50472383649915],\n",
       " [9.03126831761447e-8, -0.513866371402855, 1.50970774622550],\n",
       " [8.51754154260564e-8, -0.527318936804468, 1.51440539543471],\n",
       " [7.99587229270723e-8, -0.540690976176139, 1.51881713483111],\n",
       " [7.46665114982200e-8, -0.553980161942494, 1.52294326222873],\n",
       " [6.93027067003306e-8, -0.567184065591964, 1.52678402829294],\n",
       " [6.38712485598778e-8, -0.580300162940271, 1.53033964188431],\n",
       " [5.83760858088279e-8, -0.593325839475324, 1.53361027501584],\n",
       " [5.28211696773659e-8, -0.606258395782494, 1.53659606743300],\n",
       " [4.72104472902369e-8, -0.619095053046802, 1.53929713082415],\n",
       " [4.15478547026988e-8, -0.631832958626167, 1.54171355266769],\n",
       " [3.58373096341990e-8, -0.644469191687695, 1.54384539972064],\n",
       " [3.00827039459632e-8, -0.657000768896845, 1.54569272115275],\n",
       " [2.42878959180062e-8, -0.669424650147373, 1.54725555132906],\n",
       " [1.84567023591762e-8, -0.681737744318117, 1.54853391224305],\n",
       " [1.25928906222225e-8, -0.693936915041027, 1.54952781560213],\n",
       " [6.70017055988249e-9, -0.706018986463307, 1.55023726456661],\n",
       " [7.82186478800858e-10, -0.717980748985187, 1.55066225514282],\n",
       " [-5.15749086882152e-9, -0.729818964953675, 1.55080277723085],\n",
       " [-1.11153721981687e-8, -0.741530374291595, 1.55065881532718],\n",
       " [-1.70880574742129e-8, -0.753111700040414, 1.55023034888205],\n",
       " [-2.30722435093694e-8, -0.764559653794685, 1.54951735231153],\n",
       " [-2.90647313521181e-8, -0.775870941005458, 1.54851979466407],\n",
       " [-3.50624334136804e-8, -0.787042266129718, 1.54723763894082]]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "front_right_joint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "fbf4be9e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[0.0, -0.7, 1.5],\n",
       " [-1.41374293044852e-9, -0.702876631544616, 1.50000626606623],\n",
       " [-2.82887576970141e-9, -0.705745230679449, 1.49999470985377],\n",
       " [-4.24535162146106e-9, -0.708605749880216, 1.49996533126797],\n",
       " [-5.66312392780936e-9, -0.711458141552086, 1.49991813014646],\n",
       " [-7.08214647354450e-9, -0.714302358034348, 1.49985310625911],\n",
       " [-8.50237339398725e-9, -0.717138351605041, 1.49977025930782],\n",
       " [-9.92375918094403e-9, -0.719966074485555, 1.49966958892626],\n",
       " [-1.13462586876943e-8, -0.722785478845191, 1.49955109467951],\n",
       " [-1.27698271363630e-8, -0.725596516805683, 1.49941477606361],\n",
       " [-1.41944201231250e-8, -0.728399140445683, 1.49926063250507],\n",
       " [-1.56199936242763e-8, -0.731193301805211, 1.49908866336019],\n",
       " [-1.70465040025226e-8, -0.733978952890049, 1.49889886791443],\n",
       " [-1.84739080128339e-8, -0.736756045676112, 1.49869124538156],\n",
       " [-1.99021628076489e-8, -0.739524532113758, 1.49846579490284],\n",
       " [-2.13312259438134e-8, -0.742284364132065, 1.49822251554602],\n",
       " [-2.27610553875683e-8, -0.745035493643054, 1.49796140630430],\n",
       " [-2.41916095200783e-8, -0.747777872545872, 1.49768246609522],\n",
       " [-2.56228471432873e-8, -0.750511452730921, 1.49738569375941],\n",
       " [-2.70547274860977e-8, -0.753236186083939, 1.49707108805931],\n",
       " [-2.84872102088163e-8, -0.755952024490029, 1.49673864767775],\n",
       " [-2.99202554094420e-8, -0.758658919837641, 1.49638837121646],\n",
       " [-3.13538236288704e-8, -0.761356824022490, 1.49602025719455],\n",
       " [-3.27878758560980e-8, -0.764045688951436, 1.49563430404679],\n",
       " [-3.42223735339681e-8, -0.766725466546286, 1.49523051012192],\n",
       " [-3.56572785631826e-8, -0.769396108747563, 1.49480887368078],\n",
       " [-3.70925533093496e-8, -0.772057567518199, 1.49436939289441],\n",
       " [-2.84982687630446e-8, -0.790969341041965, 1.53334744777642],\n",
       " [-1.87063511845426e-8, -0.807224576154768, 1.57158758087303],\n",
       " [-7.69736490222839e-9, -0.820470369959396, 1.60855374884627],\n",
       " [4.53195605129227e-9, -0.830396889586483, 1.64372202761123],\n",
       " [1.79563877528850e-8, -0.836748931152672, 1.67658324453533],\n",
       " [3.25077283810906e-8, -0.839338602868788, 1.70664724320425],\n",
       " [4.80588623307917e-8, -0.838058293668730, 1.73344912968178],\n",
       " [6.44079275726939e-8, -0.832892621119666, 1.75655762078917],\n",
       " [8.12651786250931e-8, -0.823927654117265, 1.77558531662164],\n",
       " [9.82461317461746e-8, -0.811355513254500, 1.79020036204984],\n",
       " [1.14875064715458e-7, -0.795472612351211, 1.80013858756970],\n",
       " [1.30602353476095e-7, -0.776670418682595, 1.80521490495686],\n",
       " [1.44837057380905e-7, -0.755418658299168, 1.80533257525865],\n",
       " [1.56992734153933e-7, -0.732242191916815, 1.80048905295351],\n",
       " [1.66540544985557e-7, -0.707694006900634, 1.79077747599917],\n",
       " [1.73060738437005e-7, -0.682327544241287, 1.77638346866147],\n",
       " [1.76282946769696e-7, -0.656671653786483, 1.75757762079629],\n",
       " [1.76107914784583e-7, -0.631210827638336, 1.73470462947900],\n",
       " [1.72607617132744e-7, -0.606372224907207, 1.70817048482654],\n",
       " [1.66005622645220e-7, -0.582519731367125, 1.67842917769270],\n",
       " [1.56643374456564e-7, -0.559954234338908, 1.64597022414147],\n",
       " [1.44939791517903e-7, -0.538918635818307, 1.61130793244725],\n",
       " [1.31351226745577e-7, -0.519605903933319, 1.57497289875165],\n",
       " [1.16337008743745e-7, -0.502168576916797, 1.53750580430949],\n",
       " [1.00333447719942e-7, -0.486728437104455, 1.49945325650783],\n",
       " [9.53666448414560e-8, -0.500335501426890, 1.50472383649915],\n",
       " [9.03126831795240e-8, -0.513866371402855, 1.50970774622550],\n",
       " [8.51754154287852e-8, -0.527318936804468, 1.51440539543471],\n",
       " [7.99587229291505e-8, -0.540690976176139, 1.51881713483111],\n",
       " [7.46665115002982e-8, -0.553980161942494, 1.52294326222873],\n",
       " [6.93027067021920e-8, -0.567184065591964, 1.52678402829294],\n",
       " [6.38712485615223e-8, -0.580300162940271, 1.53033964188431],\n",
       " [5.83760858104724e-8, -0.593325839475324, 1.53361027501584],\n",
       " [5.28211696792272e-8, -0.606258395782494, 1.53659606743300],\n",
       " [4.72104472920983e-8, -0.619095053046802, 1.53929713082415],\n",
       " [4.15478547045602e-8, -0.631832958626167, 1.54171355266769],\n",
       " [3.58373096360604e-8, -0.644469191687695, 1.54384539972064],\n",
       " [3.00827039478246e-8, -0.657000768896845, 1.54569272115275],\n",
       " [2.42878959198676e-8, -0.669424650147373, 1.54725555132906],\n",
       " [1.84567023610376e-8, -0.681737744318117, 1.54853391224305],\n",
       " [1.25928906236502e-8, -0.693936915041027, 1.54952781560213],\n",
       " [6.70017056131019e-9, -0.706018986463307, 1.55023726456661],\n",
       " [7.82186480228558e-10, -0.717980748985187, 1.55066225514282],\n",
       " [-5.15749086739382e-9, -0.729818964953675, 1.55080277723085],\n",
       " [-1.11153721967410e-8, -0.741530374291595, 1.55065881532718],\n",
       " [-1.70880574723515e-8, -0.753111700040414, 1.55023034888205],\n",
       " [-2.30722435075081e-8, -0.764559653794685, 1.54951735231153],\n",
       " [-2.90647313498230e-8, -0.775870941005458, 1.54851979466407],\n",
       " [-3.50624334118190e-8, -0.787042266129718, 1.54723763894082]]"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "back_left_joint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "9bde0252",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[0.0, -0.7, 1.5],\n",
       " [-1.41374293044852e-9, -0.702876631544616, 1.50000626606623],\n",
       " [-2.82887576948457e-9, -0.705745230679449, 1.49999470985377],\n",
       " [-4.24535162135264e-9, -0.708605749880216, 1.49996533126797],\n",
       " [-5.66312392759252e-9, -0.711458141552086, 1.49991813014646],\n",
       " [-7.08214647332766e-9, -0.714302358034348, 1.49985310625911],\n",
       " [-8.50237339387883e-9, -0.717138351605041, 1.49977025930782],\n",
       " [-9.92375918083561e-9, -0.719966074485555, 1.49966958892626],\n",
       " [-1.13462586876943e-8, -0.722785478845191, 1.49955109467951],\n",
       " [-1.27698271362546e-8, -0.725596516805683, 1.49941477606361],\n",
       " [-1.41944201230166e-8, -0.728399140445683, 1.49926063250507],\n",
       " [-1.56199936240595e-8, -0.731193301805211, 1.49908866336019],\n",
       " [-1.70465040024142e-8, -0.733978952890049, 1.49889886791443],\n",
       " [-1.84739080127255e-8, -0.736756045676112, 1.49869124538156],\n",
       " [-1.99021628076489e-8, -0.739524532113758, 1.49846579490284],\n",
       " [-2.13312259439219e-8, -0.742284364132065, 1.49822251554602],\n",
       " [-2.27610553876767e-8, -0.745035493643054, 1.49796140630430],\n",
       " [-2.41916095201867e-8, -0.747777872545872, 1.49768246609522],\n",
       " [-2.56228471433957e-8, -0.750511452730921, 1.49738569375941],\n",
       " [-2.70547274863146e-8, -0.753236186083939, 1.49707108805931],\n",
       " [-2.84872102090331e-8, -0.755952024490029, 1.49673864767775],\n",
       " [-2.99202554096588e-8, -0.758658919837641, 1.49638837121646],\n",
       " [-3.13538236291957e-8, -0.761356824022490, 1.49602025719455],\n",
       " [-3.27878758565317e-8, -0.764045688951436, 1.49563430404679],\n",
       " [-3.42223735345102e-8, -0.766725466546286, 1.49523051012192],\n",
       " [-3.56572785638332e-8, -0.769396108747563, 1.49480887368078],\n",
       " [-3.70925533098917e-8, -0.772057567518199, 1.49436939289441],\n",
       " [-2.84982687649492e-8, -0.790969341041965, 1.53334744777642],\n",
       " [-1.87063511864472e-8, -0.807224576154768, 1.57158758087303],\n",
       " [-7.69736490347312e-9, -0.820470369959396, 1.60855374884627],\n",
       " [4.53195605004754e-9, -0.830396889586483, 1.64372202761123],\n",
       " [1.79563877513121e-8, -0.836748931152672, 1.67658324453533],\n",
       " [3.25077283795177e-8, -0.839338602868788, 1.70664724320425],\n",
       " [4.80588623287525e-8, -0.838058293668730, 1.73344912968178],\n",
       " [6.44079275711795e-8, -0.832892621119666, 1.75655762078917],\n",
       " [8.12651786235788e-8, -0.823927654117265, 1.77558531662164],\n",
       " [9.82461317446603e-8, -0.811355513254500, 1.79020036204984],\n",
       " [1.14875064714365e-7, -0.795472612351211, 1.80013858756970],\n",
       " [1.30602353475002e-7, -0.776670418682595, 1.80521490495686],\n",
       " [1.44837057380492e-7, -0.755418658299168, 1.80533257525865],\n",
       " [1.56992734153476e-7, -0.732242191916815, 1.80048905295351],\n",
       " [1.66540544985691e-7, -0.707694006900634, 1.79077747599917],\n",
       " [1.73060738437349e-7, -0.682327544241287, 1.77638346866147],\n",
       " [1.76282946770928e-7, -0.656671653786483, 1.75757762079629],\n",
       " [1.76107914785163e-7, -0.631210827638336, 1.73470462947900],\n",
       " [1.72607617133324e-7, -0.606372224907207, 1.70817048482654],\n",
       " [1.66005622646033e-7, -0.582519731367125, 1.67842917769270],\n",
       " [1.56643374456776e-7, -0.559954234338908, 1.64597022414147],\n",
       " [1.44939791517788e-7, -0.538918635818307, 1.61130793244725],\n",
       " [1.31351226744320e-7, -0.519605903933319, 1.57497289875165],\n",
       " [1.16337008740000e-7, -0.502168576916797, 1.53750580430949],\n",
       " [1.00333447715479e-7, -0.486728437104455, 1.49945325650783],\n",
       " [9.53666448374262e-8, -0.500335501426890, 1.50472383649915],\n",
       " [9.03126831761447e-8, -0.513866371402855, 1.50970774622550],\n",
       " [8.51754154260564e-8, -0.527318936804468, 1.51440539543471],\n",
       " [7.99587229270723e-8, -0.540690976176139, 1.51881713483111],\n",
       " [7.46665114982200e-8, -0.553980161942494, 1.52294326222873],\n",
       " [6.93027067003306e-8, -0.567184065591964, 1.52678402829294],\n",
       " [6.38712485598778e-8, -0.580300162940271, 1.53033964188431],\n",
       " [5.83760858088279e-8, -0.593325839475324, 1.53361027501584],\n",
       " [5.28211696773659e-8, -0.606258395782494, 1.53659606743300],\n",
       " [4.72104472902369e-8, -0.619095053046802, 1.53929713082415],\n",
       " [4.15478547026988e-8, -0.631832958626167, 1.54171355266769],\n",
       " [3.58373096341990e-8, -0.644469191687695, 1.54384539972064],\n",
       " [3.00827039459632e-8, -0.657000768896845, 1.54569272115275],\n",
       " [2.42878959180062e-8, -0.669424650147373, 1.54725555132906],\n",
       " [1.84567023591762e-8, -0.681737744318117, 1.54853391224305],\n",
       " [1.25928906222225e-8, -0.693936915041027, 1.54952781560213],\n",
       " [6.70017055988249e-9, -0.706018986463307, 1.55023726456661],\n",
       " [7.82186478800858e-10, -0.717980748985187, 1.55066225514282],\n",
       " [-5.15749086882152e-9, -0.729818964953675, 1.55080277723085],\n",
       " [-1.11153721981687e-8, -0.741530374291595, 1.55065881532718],\n",
       " [-1.70880574742129e-8, -0.753111700040414, 1.55023034888205],\n",
       " [-2.30722435093694e-8, -0.764559653794685, 1.54951735231153],\n",
       " [-2.90647313521181e-8, -0.775870941005458, 1.54851979466407],\n",
       " [-3.50624334136804e-8, -0.787042266129718, 1.54723763894082]]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "back_right_joint"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
